Question

In a sports club, 65% of children play football, 70% play volleyball and 75% play basketball. What is the smallest percentage of children playing all these three games? 

Answer 1

Out of 100 children, the total number of children who do not play

(i)  football = 100 – 65 = 35

(ii)  volleyball = 100 – 70 = 30

(iii)  basketball = 100 – 75 = 25

So, the maximum number of children who do not play at least one game is

35 + 30 + 25 = 90

Thus, the minimum number of children who play all three games is

100 - 90 = 10

Hence, the smallest percentage of children playing all three games is 10%.

Note: The greatest percentage of children playing all three games = min(65%, 70%, 75%) = 65%.